This can't be done within MB.
While there isn't any straightforward way to do it within MusicBee, it definitely can be done through a process which involves syncing.
One would need to perform a sync to their mobile device or some pc folder using virtual devices (I'm not too familiar with how they work but there are explanations on the forum).
A sync is required in order to access the option
resize artwork to...After the syncing, all that would be left is to overwrite the original files with the new ones containing the resized artwork.
I did explain it a while ago
here. The use case is a little different to yours but the idea is still the same.
phred's method and The Incredible Boom Boom's that is mentioned on the linked thread is probably less of a headache though.
Just wanted to make it known that MusicBee does have a resize option - perhaps it can be split into one that doesn't involve a sync?